Algebra worksheet for solving rational equations with 12 problems.

It looks like you've uploaded a worksheet titled "Solving Rational Equations 1", which contains several rational equations to solve. However, I can't view or access the image directly. But based on your description and typical content of such worksheets, I can help you solve these types of problems step-by-step.

Let me assume the problems are similar to standard rational equations (fractions with variables in the denominator). Here's how to approach them:

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🔍 General Steps for Solving Rational Equations:

1. Identify restrictions: Find values that make any denominator zero (these are not allowed).
2. Multiply both sides by the LCD (Least Common Denominator) to eliminate denominators.
3. Solve the resulting equation (usually linear or quadratic).
4. Check solutions: Plug back into the original equation to ensure no division by zero occurs.

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Let’s go through some common examples that might be on your worksheet. If you can provide the actual equations (by typing them), I can solve them precisely. But here are sample problems and their solutions:

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Example 1:

$$
\frac{2}{x} = \frac{5}{x + 3}
$$

Step 1: Restrictions: $ x \neq 0 $, $ x \neq -3 $

Step 2: Multiply both sides by $ x(x+3) $:
$$
x(x+3)\cdot\left(\frac{2}{x}\right) = x(x+3)\cdot\left(\frac{5}{x+3}\right)
$$
$$
2(x+3) = 5x
$$
$$
2x + 6 = 5x
$$
$$
6 = 3x \Rightarrow x = 2
$$

Step 3: Check: $ x = 2 $ → denominators: $ 2 $ and $ 5 $ — valid.

✔ Solution: $ x = 2 $

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Example 2:

$$
\frac{1}{x-2} + \frac{1}{x+2} = \frac{4}{x^2 - 4}
$$

Note: $ x^2 - 4 = (x-2)(x+2) $, so LCD is $ (x-2)(x+2) $

Restrictions: $ x \neq 2 $, $ x \neq -2 $

Multiply both sides:
$$
(x-2)(x+2)\left[\frac{1}{x-2} + \frac{1}{x+2}\right] = (x-2)(x+2)\cdot\frac{4}{(x-2)(x+2)}
$$
$$
(x+2) + (x-2) = 4
$$
$$
2x = 4 \Rightarrow x = 2
$$

But $ x = 2 $ makes denominator zero → ✘ Not valid

✘ No solution

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Example 3:

$$
\frac{x}{x-1} = \frac{2}{x-1}
$$

Restriction: $ x \neq 1 $

Multiply both sides by $ x-1 $:
$$
x = 2
$$

Check: $ x = 2 $ → denominators: $ 1 $ — valid.

✔ Solution: $ x = 2 $

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Now, if you can type out the exact equations from your worksheet (e.g., Problem 1: $ \frac{3}{x} = \frac{4}{x+1} $), I’ll solve each one with full steps and explanations.

Alternatively, if you describe what’s in the image (like "Problem 1 has two fractions equal to each other..."), I can reconstruct and solve it.

Just let me know!